My realtor said no fridge or laundry machines because of liability issue, but throughout the years of renting myself I never had to bring in my own fridge and laundry machines.

IF they even own the asset .. not get their doc's and deeds and all sorts of other VERY routine aspects of a real estate transactions just screams of amateur hour.. and the marketing company just throwing up as much as will stick make their money have no back end liability and laugh all the way to the bank. 

I don't see a lot of mid west rental houses leveraged to the max as being targets personally.I know in our building side we pay a bunch for liability .. this is far more real than the outlier like described above that is the one in a million chance or event..

Liability.  

Transfer of interest in an LLC has no bearing on the liabilities of the LLC. 

Which is 90% On my Income/net worth and just 10% on my Expenses/liabilities.

The following activities of a foreign limited liability company do NOT constitute transacting business within the meaning of the New Mexico Limited Liability Company Act:a. maintaining, defending or settling any proceeding;c. maintaining bank accounts;e. selling through independent contractors;f. soliciting or obtaining orders whether by mail or through employees or agents or otherwise, if the orders require acceptance outside New Mexico before they become contracts;g. creating as borrower or lender or acquiring indebtedness or mortgages or other security interests in real or personal property;h. securing or collecting debts or enforcing rights in property securing debts;i. investing in or acquiring, in transactions outside New Mexico, royalties and other nonoperating mineral interests; executing division orders, contracts of sale and other instruments incidental tothe ownership of such nonoperating mineral interests; and, in general, owning, without more, real or personal property; j. conducting an isolated transaction that is completed within thirty days and that is not one in the course of repeated transactions of a like nature; ------------Nor shall a foreign limited liability company be considered to be transacting business in New Mexico solely because it:1) owns a controlling interest in a corporation or a foreign corporation that transacts business in New Mexico;2) is a limited partner of a limited partnership or foreign limited partnership that is transacting business in New Mexico; or3) is a member or manager of a limited liability company or foreign limited liability company that is transacting business in New Mexico. ----------------------------------------* as per note above:b. holding meetings of its members or carrying on any other activities concerning its internal affairs;d. maintaining offices or agencies for the transfer, exchange and registration of the foreign limited liability company’s own securities or interests or appointing and maintaining trustees or depositories with respect to those securities or interests;k. transacting business in interstate commerce"

Now think about errors and omissions insurance, professional liability coverage that is required for the broker and agents.

I have no idea what your liability would look like because they are just a contractor who happens to be your tenant. 

Two-fold question: 1) Is the water claim something I should be worried about from a liability standpoint or if it was fixed properly it shouldn't be an issue?